Grades 9 through 12

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CCSS Lessons Grades 9 through 12

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Number and Quantity Overview


The Real Number System

  • Extend the properties of exponents to rational exponents
  • Use properties of rational and irrational numbers.

Quantities

  • Reason quantitatively and use units to solve problems

The Complex Number System

  • Perform arithmetic operations with complex numbers
  • Represent complex numbers and their operations on the complex plane
  • Use complex numbers in polynomial identities and equations

Vector and Matrix Quantities

  • Represent and model with vector quantities.
  • Perform operations on vectors.
  • Perform operations on matrices and use matrices in applications.


Algebra Overview


Seeing Structure in Expressions

  • Interpret the structure of expressions
  • Write expressions in equivalent forms to solve problems

Arithmetic with Polynomials and Rational Expressions

  • Perform arithmetic operations on polynomials
  • Understand the relationship between zeros and factors of polynomials
  • Use polynomial identities to solve problems
  • Rewrite rational expressions

Creating Equations

  • Create equations that describe numbers or relationships

Reasoning with Equations and Inequalities

  • Understand solving equations as a process of reasoning and explain the reasoning
  • Solve equations and inequalities in one variable
  • Solve systems of equations
  • Represent and solve equations and inequalities graphically


Functions Overview


Interpreting Functions

  • Understand the concept of a function and use function notation
  • Interpret functions that arise in applications in terms of the context
  • Analyze functions using different representations

Building Functions

  • Build a function that models a relationship between two quantities
  • Build new functions from existing functions Linear, Quadratic, and Exponential Models
  • Construct and compare linear, quadratic, and exponential models and solve problems
  • Interpret expressions for functions in terms of the situation they model

Trigonometric Functions

  • Extend the domain of trigonometric functions using the unit circle
  • Model periodic phenomena with trigonometric functions
  • Prove and apply trigonometric identities


Geometry Overview


Congruence

  • Experiment with transformations in the plane
  • Understand congruence in terms of rigid motions
  • Prove geometric theorems
  • Make geometric constructions

Similarity, Right Triangles, and Trigonometry

  • Understand similarity in terms of similarity transformations
  • Prove theorems involving similarity
  • Define trigonometric ratios and solve problems involving right triangles
  • Apply trigonometry to general triangles

Circles

  • Understand and apply theorems about circles
  • Find arc lengths and areas of sectors of circles

Expressing Geometric Properties with Equations

  • Translate between the geometric description and the equation for a conic section
  • Use coordinates to prove simple geometric theorems algebraically

Geometric Measurement and Dimension

  • Explain volume formulas and use them to solve problems
  • Visualize relationships between two-dimensional and three-dimensional objects

Modeling with Geometry

  • Apply geometric concepts in modeling


Statistics and Probability Overview


Interpreting Categorical and Quantitative Data

  • Summarize, represent, and interpret data on a single count or measurement variable
  • Summarize, represent, and interpret data on two categorical and quantitative variables
  • Interpret linear models

Making Inferences and Justifying Conclusions

  • Understand and evaluate random processes underlying statistical experiments
  • Make inferences and justify conclusions from sample surveys, experiments and observational studies

Conditional Probability and the Rules of Probability

  • Understand independence and conditional probability and use them to interpret data
  • Use the rules of probability to compute probabilities of compound events in a uniform probability model

Using Probability to Make Decisions

  • Calculate expected values and use them to solve problems
  • Use probability to evaluate outcomes of decisions